PlayOnLinux is more of a front-end to manage Wine. By default, it'll use the system installation of Wine, but it's not an absolute requirement since PlayOnLinux can install releases of Wine. Their idea of having different Wine versions is that some programs may work better under older versions of Wine.
If you'd like the latest release of Wine, the WineHQ team themselves have an official PPA for Ubuntu which you can install:
Historically, the Boutique did have Wine listed on its own... they will have been a reason why it was removed. 
I think at the time, there wasn't an official Wine repository, but there was an unofficial "Ubuntu" PPA that was unmaintained for a long time. Another issue is that you could install Wine on its own, but it's not obvious how it's used as it's not shown in the application menu.
There is a wine package in the Ubuntu repositories (outside of Boutique), which can be installed using one of the software managers listed under Boutique's More Software category. Unfortunately, that particular package ends up a few versions behind.
Sounds more like an objective for a Linux distribution like Zorin OS. Ubuntu MATE has a different set of objectives with a different solution to a mission (preserving and modernising the traditional Linux desktop). 
In my view, Ubuntu MATE has its signature 
Welcome program to inform new users, rather then promote compatibility with Windows software. Compromises may need to be made; alternate software to be found; and Wine is good at crossing the bridge. As you've pointed out, we can improve this experience and expectation in the Boutique.
This is also an interesting read:
If you are facing difficulties with a certain application under Wine, feel free to ask the community!